The main aim of this paper is to investigate the nature of the two brightest hotspots of Cygnus A by using the high angular resolution and large observed bandwidth provided by LOFAR. It is clear from the spectral index map that both of the main hotspots have inverted radio spectra between 109 and 183 MHz. The average spectral index of hotspot D in the LOFAR band is \(\alpha = +\) 0.36 \(\pm \)  0.02 and for hotspot A is \(\alpha = +\) 0.18 \(\pm \)  0.01, as measured at the position of the peak surface brightness emission in the total intensity map for each hotspot. In Fig. REF , we show the spectral energy distribution of the hotspots A and D from combining the LOFAR data between 109 and 183 MHz with the measurements made with the VLA between 327.5 MHz and 22.45 GHz by [1]}. We see that the spectra of hotspots A and D turnover at around 140 and 160 MHz, respectively. This is the first time that such a turnover has been directly observed for both of the hotspots of Cygnus A. We also note that the average spectral index for hotspot B in the LOFAR band is \(\alpha = -\) 0.26 \(\pm \)  0.01, which is likely a lower limit due to contamination from the steep spectrum lobe emission. The spectral indices of hotspots A, B, and D are all confirmed to be flatter than is predicted from diffusive shock acceleration models [2]}. These measurements highlight the important role LOFAR can have in measuring the arcsecond-scale spectra of radio-loud active galaxies at low radio frequencies.
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